Unsupervised Dimension Selection using a Blue Noise Spectrum

Abstract: Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional embeddings, they produce feature spaces that are hard to interpret. Further, in applications such as sensor design, one needs to perform reduction directly in the input domain, instead of constructing transformed spaces. Consequently, dimension selection (DS) aims to solve the combinatorial problem of identifying the top-$k$ dimensions, which is required for effective experiment design, reducing data while keeping it interpretable, and designing better sensing mechanisms. In this paper, we develop a novel approach for DS based on graph signal analysis to measure feature influence. By analyzing synthetic graph signals with a blue noise spectrum, we show that we can measure the importance of each dimension. Using experiments in supervised learning and image masking, we demonstrate the superiority of the proposed approach over existing techniques in capturing crucial characteristics of high dimensional spaces, using only a small subset of the original features.